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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

1 vote
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256 views

Section ring $R(X,D)$ of $D$ is finitely generated if $\kappa (X,D) \leq 1$

In the remark on the bottom of page 5 of this paper, the author states that It is well-known fact that the algebra of a Divisor $D$ with $\kappa (X,D) \leq 1$ is finitely generated over $k$. In …
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5 votes
0 answers
240 views

Map associated to linear system onto curve is morphism

In Mumford's first paper on Surfaces in char $p$ [1], part 2 Step (II), he wants to show that, given an indecomposable curve of canonical type $D$ on a smooth projective surface $F$ with $p_g(F)=0, K_ …
numberjedi's user avatar